Solve for $x$ and $y$ using elimination. ${2x-3y = -28}$ ${-5x+3y = 25}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {2x-3y = -28}\thinspace$ to find $y$ ${2}{(1)}{ - 3y = -28}$ $2-3y = -28$ $2{-2} - 3y = -28{-2}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {-5x+3y = 25}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ + 3y = 25}$ ${y = 10}$